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RoseWind [281]
3 years ago
12

Sam the scout is going on a camp out with his boy-scout troop. There are large tents that sleep 6 boys and small tents that slee

p 4 boys. The ratio of large tents to small tents is 8 to 5. There are exactly enough tents to sleep 816 boys. How many tents of each size are there?
Mathematics
1 answer:
natita [175]3 years ago
5 0

Answer:

There are 96 large tents and 60 small tents

Step-by-step explanation:

Here, we want to calculate the number of tents of each sizes there

Let the number of 6-boys tent be s and the number of 4-boys tent be f

6s + 4f = 816 ••••••(i)

Ratio of large to small ( ratio of s to f)

8:5 = s/f

8/5 = s/f

8f = 5s

f = 5s/8 ••••(ii)

Substitute ii into i

6s + 4(5s/8) = 816

6s + 5s/2 = 816

Multiply through by 2

12s + 5s = 1,632

17s = 1632

s = 1632/17

s = 96

f = 5s/8

f = (5 * 96)/8 = 60

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Answer:

So, The possible values of h and r are

1. r = 3 , h = 3

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Step-by-step explanation:

P.S - The exact ques is -

As we know that Volume of cone , V = \frac{1}{3}\pi r^{2}h

As given,

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⇒\frac{1}{3}\pi r^{2}h = 9\pi \\  \frac{1}{3} r^{2}h = 9 \\r^{2}h = 27

So,

The possible values of h and r are

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In Case I-

When r = 3, h = 3

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Case II-

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Satisfied

Case III-

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Satisfied

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